Simplify the following expression: $z = \dfrac{a^2 + a - 12}{a + 4} $
First factor the polynomial in the numerator. $ a^2 + a - 12 = (a + 4)(a - 3) $ So we can rewrite the expression as: $z = \dfrac{(a + 4)(a - 3)}{a + 4} $ We can divide the numerator and denominator by $(a + 4)$ on condition that $a \neq -4$ Therefore $z = a - 3; a \neq -4$